Just a bit of background info. If f:S^2 --> R is a continuous mapping, then as a special case of the Borsuk-Ulam theorem (you don't need to know this), there exists c in S^2 such that f(c) = f(-c). S^2 just means 2 sphere, which is just what it sounds like - a sphere. So basically, I have a continuous function f(x) =...blah.... such that f(c) = f(-c) for some c in the domain. Suppose f measures the intensity of sunlight at each point on the earth's surface(so S^2 is the earth's surface), then it follows (from what I wrote above), that there exists a pair of points opposite each other on the earth's surface at which sunlight intensity is the same, but if it is daytime at one point, it's night time at the point opposite! Resolve the paradox.